Multi-objective Optimal Block Transaction model based Transient Stability Evaluation

Transcription

1 Proceedngs of the 5th WSEAS Internatona Conference on Aed Comuter Scence, Hangzhou, Chna, Ar 6-8, 006 (907-9) Mut-objectve Otma Boc Transacton mode based Transent Stabty Evauaton Ru Ma, Hongwen Yan Changsha Unversty of Scence and Technoogy Chng Road 45, Changsha, Chna Abstract: - Ths aer resents a nove mut-objectve otmzaton boc bddng mode for ower marets, whch tae the mnmum of the oo urchase cost and the mnmum outon emsson nto consderaton. Frsty, two snge-objectve robem s soved and the vaue of objectve functon are ganed, then by usng fuzzy sets theory the mut-objectve robem s reformuated nto a new standard snge-objectve nonnear rogrammng robem by means of max-mn oerator, fnay, the new bddng resuts that mut-objectve otma s ganed by the queung agorthm. To evauate the feasbty of the transacton annng, the transent stabty smuaton for mut-objectve otma transacton schedung s aso nvestgated n ths aer. The numerca resuts of IEEE 9-bus 3 generator system shows the effcency of the roosed mode and agorthm. Ths mode can get envronmenta/economc otmzaton under the system transent stabty and can ensure the farness of mut-factor of generaton bdder n eectrcty maret. Key-Words: - boc bddng mode, eectrcty maret; mut-objectve otma; transacton schedung; transent stabty Introducton In recent years, the eectrcty ndustry has undergone drastc changes due to a word wde dereguaton or rvaton rocess that has sgnfcanty affected energy maret. Bddng mechansm s one of the most chaenge ssues n the ower maret. Houry bddng s the wdey used bddng mechansm n resent ower marets[-], by whch oad demand s dvded and auctoned hour by hour(or haf hour by haf hour)to form sot rce. However, some shortcomngs[3], such as uncertanty, randomness of unt commtment, rces ses, arse because of the nconsstence of the bddng rues wth the contnuty features of eectrc energy roducton. Therefore, Bocng Bddng mechansm s resented by author of[3-5], Boc bddng dvdes the demand the demand oad nto mute bocs wth contnuous segment and the aucton s erformed for each boc, Ths bddng mechansm s consstent wth features of eectrc energy roducton and consummaton, whch s more convenent for oeratng ower marets[4]. However, the mnmum of oo urchase cost or maxmum of soca beneft s maret cearng snge objectve n houry or boc bddng at resent ower maret. Ths wor s artay suorted by the Hunan Provnce Scence Foundaton Grant #05JJ40088 and the Foundatona Research Funds of Changsha Unversty of Scence and Technoogy. In addton, the ncreasng ubc awareness of the envronment rotecton and the assage of the Cear Ar Act Amendments of 990 have forced the uttes to modfy ther desgn or oeratons strateges to reduce outon and atmosherc emssons of the therma ower ants. Severa strateges to reduce the atmosherc emsson have dscussed[6-8]. These ncude nstaaton of outant cearng equment, swtchng to ow emsson fues, reacement of the aged fue-burners wth cearer ones, and the Envronmenta/Economc ower dsatchng. A mut-objectve fuzzy otma short-term transacton annng consderng envronment rotecton and economc roft n the dereguated ower system by the author[7], However, ths mode based on the houry bddng mechansm. Nove mut-objectve boc and grou bddng mode for hydrotherma ower maret s aso roosed by the author[8], but not evauated the transent stabty for transacton annng. whereas, transent stabty s the recondton of mement for transacton schedung that decded by the houry or boc bddng, Therefore, the transacton schedung must been evauated through the transent stabty based on the reaty of system. Ths aer resents a mut-objectve otmzaton boc bddng mode for ower marets, whch tae nto the mnma of the oo urchase cost and the mnma emsson of the outon consderaton. Frsty, two snge-objectve robem s soved by

2 Proceedngs of the 5th WSEAS Internatona Conference on Aed Comuter Scence, Hangzhou, Chna, Ar 6-8, 006 (907-9) nteror ont agorthm and the vaue of objectve functon are ganed, then by usng fuzzy sets theory the mut-objectve robem s reformuated nto a new standard snge-objectve nonnear rogrammng robem by means of max-mn oerator, Fnay, the new bddng resuts that mut-objectve otma s ganed by sovng ths mode. Transent stabty evauaton for transacton schedung s aso nvestgated n ths aer. The smuated resuts of IEEE 9-bus 3-generators system shows that the roosed mode and aroach can made mut-objectve otmzaton and can ensure the farness of mut-factor of generaton bdder n eectrcty maret. MATHEMATICAL MODEL OF MULTI- OBJECTIVE OPTIMAL BLOCK BIDDING The envronmenta/economc otma boc bddng robem s to mnmze two cometng objectve functons, oo urchase cost and emsson, whe satsfyng severa equaty and nequaty constrants. that s, Maret Oerator(MO) urchase ow-rce and ow-emsson ower to suy oad demand, Generay the robem s formuated as foows.. Probem Objectve Functons Mnmzaton of the oo urchase cost: the tota $ can be exressed as () mn f mn b s = = = I = () Where, are the numbers and tota numbers of bddng unt;, L s the numbers and tota numbers of oad demand boc;, K are the numbers and tota numbers of bddng rce boc; b ( ) stand for the bddng rce of unt n boc rce and oad boc, t s hysca unt s $/MWh; ( ) reresents for the bddng caacty of unt n boc rce and oad boc, the hysca unt s MW; s ( ) s the urchased state for ower boc (), f s =,then () s urchased, f s = 0,then () s not urchased. Mnmzaton of emsson: the atmosherc outants such as suher oxdes SO x and ntrogen oxdes NO x caused by foss-fueed therma unts can be modeed searatey. However tota ton emsson can be exressed as () mn f mn ( α + β + γ ) s ( ) () = = = = where γ, β, α are coeffcents of th bddng unt emsson characterstcs.. Objectve Constrants Actve ower baance constrants: For stabe oeraton, tota ower generaton must cover the tota oad demand n each oad boc, Hence, I K (3) = ( ) s ( ) = d ( ) where d () s th boc of oad demand. Bddng unt caacty constrants For stabe oeraton, rea ower outut of each generator s restrcted by ow and uer mts n each oad boc:, mn (4),max where, mn,, max s the ow and u generaton caacty mts of the th bddng unt. Mutua excuson n boc constrants: K ( ) s ( ) (5) = = Surus bddng caacty adjust constrants: b ) = b ( ( ) f < (6) max ( ) 3 ALGORITHMS FOR MULTI-OBJECTIVE OPTIMAL BLOCK BIDDING MODEL In ths secton, we gve a aroach that combned the fuzzy sets theory and the queung theory to sove the mut-objectve otma boc bddng mode of ()-(6). STEP: Sove each snge-objectve robem resectvey. The rocess can be ntroduced as foows: sove snge-objectve for oo urchase,that s, the robem s formuated by (),(3)-(6), the oo urchase cost C 0 and bddng resuts are ganed, thus, the emsson vaue C 0 s aso can been comutaton based on equaton (); n the same way, sove snge-objectve otma boc mode for mnmzaton of emsson, the robem can be mode by (),(3)-(6), the emsson C 0 and bddng resuts are aso get, thus, the emsson vaue C 0 s aso can been comutaton based on equaton (). STEP-: Defne membersh functon for each objectve. Because of oo urchase cost and emsson are a cost ndex, that s, the smaer of objectve vaue, the better of bddng resuts. we et f ( c + δ reresents an mrecse uer bound ) 0 0

3 Proceedngs of the 5th WSEAS Internatona Conference on Aed Comuter Scence, Hangzhou, Chna, Ar 6-8, 006 (907-9) on the maxmum ermssbe oo urchase cost. δ 0 s the toerance arameter that s a measure of fuzzness n ths constrants, t s very mortant to mut-objectve otma resuts, δ 0 C 0 C 0.So we can use the foowng mathematca formuaton for ths membersh functon: f( ) c0 c + = 0 δ0 f( ) µ ( f( )) c0 < f( ) < c0 + δ0 (7) δ0 0 f( ) c0 + δ0 n the same way, we et f ( ) c0 + δ0 reresents an mrecse uer bound on the maxmum ermssbe emsson. δ 0 s the toerance arameter that s a measure of fuzzness n ths constrants, δ 0 C 0 C 0.So we can defne a near membersh functon as foows: ) c0 c + = 0 δ0 ) µ ( )) c0 < ) < c0+ δ0 (8) δ0 0 ) c0 + δ0 STEP3: Bud a fuzzy boc bddng mode.based on the fuzzy set theory and max-mn oerator,ths robem can be formuated as foows: Objectve mn µ (9) Constrants: b s + 0µ C0 = = = ( + β ( ) + γ ( )) s ( ) + δ 0 µ C0 = = = 0 δ (0) α () µ () (3)-(6) STEP4: Use the queung agorthm to sove the new snge-objectve boc mode s bud by ste3,thus, the bddng resuts that match wth the two objectve are ganed. STEP5: Power fow comutaton for transacton annng based system reaty STEP6: The transent stabty of transacton annng have been evauated n each oad boc eve. f, transacton annng s transent stabty consderng system reaty,then, the annng w be execute n the eectrcty maret, otherwse, return to ste adjust bddng resuts. 4 SIMULATIONS AND ANALYSIS The roosed aroach was tested on the IEEE 9-bus 3-generator tests system n order to nvestgate ts effectveness. The snge-ne dagram of IEEE test system s shown n Fg.3 and the detaed data for ower fow and transent stabty smuatng are gven n [9], n ths system, generator s a hydroower staton, generator and 3 are two therma ower ants, thus the hydroower staton s set the base oad to bddng. Tabe s arameters of bddng unt; Tabe shows the boc of oad demand; Tabe 3 s the oad demand and Comensated reactve ; Tab.4 shows the boc bddng rce of bddng unt ; In transent stabty smuaton,we assume oad mode of each bus are 50%Z+50%IM, IM s nductor motor and mode s adoted IEEE6 IM [0], Dsturbance foows: A three-hase faut on transmsson nes 5 to 9 at nearby bus 9, the faut s ceared at the 5 cyces. unt Tabe. Parameters of Bddng Unt Ratng Lmtng of Coeffcents of Caacty rea outut emsson [MVA] [MW] [0 - ton] S N P max P mn Tabe. Boc for Load Demand Number of boc Load demand Startng tme Endng tme Contnung hour d ( ) T S (L) T E (L) T (L) [MW] [h] Tabe 3 Boc for Load Demand Bus number Load demand of each boc Comensated reactve for oad boc 5 4(boc) 85(boc) Comensat ed reactve for boc Tabe 4 The Boc Bddng Prce ofbbddng Unt Unt Unt Unt 3 b γ b β α

4 Proceedngs of the 5th WSEAS Internatona Conference on Aed Comuter Scence, Hangzhou, Chna, Ar 6-8, 006 (907-9) L7 L5 G G L9 L9 6 3 G3 Fg. IEEE 9-bus test system In smuaton resuts, Tab.5 Comarson of objectve vaue for each transacton schedung; Tabe.6 s the comarson of bddng resuts between snge-objectve and mut-objectve; Tabe.7 s the comarson of resuts of maret cearng rce(mcp) between two transacton schedung; Fg.,Fg3 and Fg4 s reatve ange curves of three oeraton annng. Fg.Reatve ange n mnmum of oo urchase cost Tabe 5 Comarson of Objectve Vaue for Each Transacton Schedung Mnmum of cost Mnmum of emsson Mut-objectve Fg3.Reatve ange n mnmum of emsson Emsson Emsson Emsson Tota Tabe.6 Comarson of Bddng Resuts Between Each Transacton Mode Wthout Networ Constrants Tabe.7 Comarson of MCP for Each Transacton Pan Mnmum of oo urchase cost Mnmum of Emsson Mut-objectve bddng Tabe. 7 Comarson of MCP for each transacton mnmum of urchase cost Mnmum of emsson Mut-obje ctve Fg4.Reatve ange n mnmum of mut-objectve To demonstrate the effectveness of the roosed mode, three dfferent cases have been smuated: the oo urchase cost and emsson objectve are otmzed ndvduay, then, the cost and emsson are otmzed based mut-objectve mode, the oo urchase cost and emsson objectves are shown n Tab.5, we can now f we tae the economc or envronmenta objectve as maret cearng objectve, we ony get a snge-objectve otmzaton bddng resuts ndvduay. However, when we tae the mut-objectve bddng mode that roosed by ths aer, we can mae the two objectve otmzed, comarson of mut-objectve bddng and mnmum of the oo urchase cost,the emsson amount s decrease 9.%,but the cost ncrease 6.034%; comarson of mut-objectve bddng and

5 Proceedngs of the 5th WSEAS Internatona Conference on Aed Comuter Scence, Hangzhou, Chna, Ar 6-8, 006 (907-9) mnmum of emsson, the emsson amount s ncrease.7%,but the cost decrease 6.59%, obvousy, ths aer can mae envronment/economc otmzed. We can now from Tab.6, because of the ow rce and ow emsson of hydroower staton, there are hgh cometton abty for hydroower n ths exame, the mut-factor farness of bddng unt are consderng n mut-objectve bddng, maret shared s based envronmenta and economc ndexes. Tab.7 shows that mut-objectve bddng mode can made tradeoff of MCP, however, the bddng mode for mnmum of oo urchase cost has a ow MCP, the bddng mode for mnmum of emsson has a hgh MCP. Accordng to the evdence avaabe form Fg.,Fg3 and Fg.4, because of the dfferent of the maer cearng objectve,the system have the dfferent curves of reatve ange. Obvousy, each transacton annng are feasbeness through transent stabty evauaton. 5 CONCLUSIONS In ths aer, a nove mut-objectve boc transacton annng mode has been resented and aed to envronmenta/economc ower dsatch otmzaton robem. The robem has been formuated as mutobjectve otmzaton wth oo urchase cost and emsson objectves. A aroach that combned fuzzy sets theory and the queung agorthm s user to sove ths robem. To evauate the feasbty of the transacton annng, the each transactons annng has been evauated by transent stabty deended on reaty of system, the resuts show that the roosed mode s effcent for sovng mutobjectve otmzaton such as envronmenta and economc n eectrcty maret. In addton, ths maret cearng mechansm made a ecectc MCP and more match wth the sustanabe deveoment stratagem of eectrc ower ndustry, ths aer can been extend to more objectves and tae nto more ractca networ constrants. IEEE Power Eng. Rev., vo., , June 00 [4] Jan Geng, Xfan Wang, Xaoyng Dng eta. Modes of boc bddng n ower maret and comarson wth houry bddng, Proceedngs of the CSEE, vo.4, no.3,.8-3, 004. [5]Xan Zhang, Xfan Wang, and Y. H. Song. Modeng and Prcng of Boc Fexbe Eectrcty Contracts. IEEE Trans. Power System., vo. 8, , 003 [6] Ru Ma. A Nove B-Objectve Fuzzy Otma Short-term Trade Pannng Mode Consderng Envronment Protecton and Economy Proft n Dereguated Power System roceedng of the CSEE, vo., no 3,.04-08,00. [7] Ru Ma, Renmu He, Hongwen Yan, Nove mut-objectve otma boc and grou bddng mode for hydrotherma ower maret. roceedng of the CSEE, vo.4, no,.53-57,004. [8] Abdo, M.A Envromenta/Economc Power Dsatch Usng Mut-objectve Evoutonary Agorthms. IEEE Trans. on Power System,Vo8,no 4, :59-537, 003 [9] Xu Dong-je, Anayss and contro of ow frequency oscaton n nterconnected ower systems, P.H.D Thess, North Chna Eectrc Power Unversty, 004. [0] IEEE Tas force on oad resentaton for Dynamc erformance.standard oad modes for ower fow and dynamc erformance smuaton. IEEE Trans on Power System, vo.0, no.3, :30-33, 995. References: [] P. Stehenson and M. Paun, Eectrcty maret tradng, Power Eng. J.,vo. 5, no. 6, , Dec. 00. [] R. Bjorgan, H. Song, C. C. Lu, and R. Dahgren, Prcng fexbe eectrcty contracts, IEEE Trans. Power Syst., vo. 5, , May 000. [3]X.Wang, X. Guan, and X.Wang, Boc rcng for eectrc ower marets,